Determine from the comps what the true value of the home is. Determine what you can reasonably afford to spend. The lower of those two numbers sets the cap at what you'll pay for the house. Not a penny more. Then determine how much you like the house...how disappointed you might be if you didn't get it. That determines how close to your maximum price you're willing to offer. But feel free to offer anything under that you wish. Yes, your chances of getting the property decrease as your offer gets lower. But that's what negotiation is all about.
Don't worry about offending a seller. Focus on acquiring a property at a good value to you.
Hope that helps.
Do consider how long the house has been on the market and try to determine the urgency of the Seller. If the Seller does not have to go anywhere he may be testing the market.
Use the market research your agent discovers to help you determine a good offer price. ~Catherine Parker